Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8036,2,Mod(1,8036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8036, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8036 = 2^{2} \cdot 7^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8036.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1677830643\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} - 30 x^{18} + 128 x^{17} + 348 x^{16} - 1644 x^{15} - 1934 x^{14} + 10948 x^{13} + \cdots + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.15720\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8036.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.15720 | −1.82281 | −0.911406 | − | 0.411509i | \(-0.865002\pi\) | ||||
−0.911406 | + | 0.411509i | \(0.865002\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.22019 | 0.992900 | 0.496450 | − | 0.868065i | \(-0.334637\pi\) | ||||
0.496450 | + | 0.868065i | \(0.334637\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.96793 | 2.32264 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.12500 | −1.24374 | −0.621868 | − | 0.783122i | \(-0.713626\pi\) | ||||
−0.621868 | + | 0.783122i | \(0.713626\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.30989 | 0.640649 | 0.320324 | − | 0.947308i | \(-0.396208\pi\) | ||||
0.320324 | + | 0.947308i | \(0.396208\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.00960 | −1.80987 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.24833 | −0.545300 | −0.272650 | − | 0.962113i | \(-0.587900\pi\) | ||||
−0.272650 | + | 0.962113i | \(0.587900\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.92368 | 0.441323 | 0.220661 | − | 0.975350i | \(-0.429178\pi\) | ||||
0.220661 | + | 0.975350i | \(0.429178\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.59856 | −0.541837 | −0.270918 | − | 0.962602i | \(-0.587327\pi\) | ||||
−0.270918 | + | 0.962602i | \(0.587327\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.0707440 | −0.0141488 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −12.5275 | −2.41093 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.54657 | 0.844277 | 0.422138 | − | 0.906531i | \(-0.361280\pi\) | ||||
0.422138 | + | 0.906531i | \(0.361280\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.881932 | 0.158400 | 0.0791998 | − | 0.996859i | \(-0.474763\pi\) | ||||
0.0791998 | + | 0.996859i | \(0.474763\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 13.0235 | 2.26709 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.08817 | 1.16529 | 0.582644 | − | 0.812727i | \(-0.302018\pi\) | ||||
0.582644 | + | 0.812727i | \(0.302018\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.29279 | −1.16778 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.1276 | −1.84945 | −0.924724 | − | 0.380637i | \(-0.875705\pi\) | ||||
−0.924724 | + | 0.380637i | \(0.875705\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 15.4701 | 2.30615 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.83253 | −0.850763 | −0.425381 | − | 0.905014i | \(-0.639860\pi\) | ||||
−0.425381 | + | 0.905014i | \(0.639860\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.09843 | 0.993980 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.01354 | −1.10074 | −0.550372 | − | 0.834920i | \(-0.685514\pi\) | ||||
−0.550372 | + | 0.834920i | \(0.685514\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.15830 | −1.23491 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.07345 | −0.804449 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 11.7512 | 1.52988 | 0.764939 | − | 0.644103i | \(-0.222769\pi\) | ||||
0.764939 | + | 0.644103i | \(0.222769\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.46459 | 0.955743 | 0.477872 | − | 0.878430i | \(-0.341408\pi\) | ||||
0.477872 | + | 0.878430i | \(0.341408\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.12840 | 0.636100 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.58808 | 0.194014 | 0.0970072 | − | 0.995284i | \(-0.469073\pi\) | ||||
0.0970072 | + | 0.995284i | \(0.469073\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.20417 | 0.987666 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.75853 | 1.03945 | 0.519723 | − | 0.854335i | \(-0.326035\pi\) | ||||
0.519723 | + | 0.854335i | \(0.326035\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.18255 | 0.255448 | 0.127724 | − | 0.991810i | \(-0.459233\pi\) | ||||
0.127724 | + | 0.991810i | \(0.459233\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.223353 | 0.0257906 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.403174 | −0.0453606 | −0.0226803 | − | 0.999743i | \(-0.507220\pi\) | ||||
−0.0226803 | + | 0.999743i | \(0.507220\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 18.6482 | 2.07202 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.26975 | 0.578430 | 0.289215 | − | 0.957264i | \(-0.406606\pi\) | ||||
0.289215 | + | 0.957264i | \(0.406606\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.99173 | −0.541429 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −14.3544 | −1.53896 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.2977 | 1.40956 | 0.704778 | − | 0.709428i | \(-0.251047\pi\) | ||||
0.704778 | + | 0.709428i | \(0.251047\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.78444 | −0.288733 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.27095 | 0.438190 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.49549 | 0.354913 | 0.177457 | − | 0.984129i | \(-0.443213\pi\) | ||||
0.177457 | + | 0.984129i | \(0.443213\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −28.7427 | −2.88875 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.26651 | −0.225526 | −0.112763 | − | 0.993622i | \(-0.535970\pi\) | ||||
−0.112763 | + | 0.993622i | \(0.535970\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.2779 | 1.01271 | 0.506355 | − | 0.862325i | \(-0.330993\pi\) | ||||
0.506355 | + | 0.862325i | \(0.330993\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.6855 | −1.12968 | −0.564839 | − | 0.825201i | \(-0.691062\pi\) | ||||
−0.564839 | + | 0.825201i | \(0.691062\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.5791 | −1.39642 | −0.698212 | − | 0.715891i | \(-0.746021\pi\) | ||||
−0.698212 | + | 0.715891i | \(0.746021\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −22.3788 | −2.12410 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.30076 | 0.404582 | 0.202291 | − | 0.979326i | \(-0.435161\pi\) | ||||
0.202291 | + | 0.979326i | \(0.435161\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.76930 | −0.537990 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 16.0952 | 1.48800 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.01565 | 0.546877 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.15720 | 0.284675 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.2580 | −1.00695 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.3254 | 1.53738 | 0.768688 | − | 0.639623i | \(-0.220910\pi\) | ||||
0.768688 | + | 0.639623i | \(0.220910\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 38.2894 | 3.37120 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.51120 | 0.743627 | 0.371814 | − | 0.928307i | \(-0.378736\pi\) | ||||
0.371814 | + | 0.928307i | \(0.378736\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −27.8136 | −2.39381 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.7219 | −1.68495 | −0.842477 | − | 0.538732i | \(-0.818903\pi\) | ||||
−0.842477 | + | 0.538732i | \(0.818903\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.78918 | −0.236575 | −0.118288 | − | 0.992979i | \(-0.537740\pi\) | ||||
−0.118288 | + | 0.992979i | \(0.537740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 18.4145 | 1.55078 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.52831 | −0.796797 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.0943 | 0.838283 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19.5417 | −1.60092 | −0.800458 | − | 0.599389i | \(-0.795410\pi\) | ||||
−0.800458 | + | 0.599389i | \(0.795410\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.15883 | 0.419820 | 0.209910 | − | 0.977721i | \(-0.432683\pi\) | ||||
0.209910 | + | 0.977721i | \(0.432683\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −15.6662 | −1.26654 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.95806 | 0.157275 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.7616 | 1.49734 | 0.748670 | − | 0.662943i | \(-0.230693\pi\) | ||||
0.748670 | + | 0.662943i | \(0.230693\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 25.3004 | 2.00645 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.9239 | −1.63888 | −0.819442 | − | 0.573163i | \(-0.805716\pi\) | ||||
−0.819442 | + | 0.573163i | \(0.805716\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 28.9146 | 2.25100 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.9531 | −0.924957 | −0.462479 | − | 0.886630i | \(-0.653040\pi\) | ||||
−0.462479 | + | 0.886630i | \(0.653040\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.66440 | −0.589569 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 13.4041 | 1.02504 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.88830 | 0.447679 | 0.223840 | − | 0.974626i | \(-0.428141\pi\) | ||||
0.223840 | + | 0.974626i | \(0.428141\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −37.1010 | −2.78868 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.1919 | 0.836524 | 0.418262 | − | 0.908326i | \(-0.362639\pi\) | ||||
0.418262 | + | 0.908326i | \(0.362639\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.6950 | 1.09227 | 0.546134 | − | 0.837698i | \(-0.316099\pi\) | ||||
0.546134 | + | 0.837698i | \(0.316099\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −23.5672 | −1.74214 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 15.7371 | 1.15702 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.27437 | 0.678209 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.75392 | 0.126909 | 0.0634547 | − | 0.997985i | \(-0.479788\pi\) | ||||
0.0634547 | + | 0.997985i | \(0.479788\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.3137 | 0.742398 | 0.371199 | − | 0.928553i | \(-0.378947\pi\) | ||||
0.371199 | + | 0.928553i | \(0.378947\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −16.1914 | −1.15949 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.69132 | −0.476737 | −0.238368 | − | 0.971175i | \(-0.576613\pi\) | ||||
−0.238368 | + | 0.971175i | \(0.576613\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.1873 | −0.863932 | −0.431966 | − | 0.901890i | \(-0.642180\pi\) | ||||
−0.431966 | + | 0.901890i | \(0.642180\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.01388 | −0.353652 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.22019 | −0.155065 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −18.1066 | −1.25849 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.93519 | −0.548889 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.7973 | 1.29406 | 0.647028 | − | 0.762466i | \(-0.276012\pi\) | ||||
0.647028 | + | 0.762466i | \(0.276012\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −27.6525 | −1.89472 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −26.9257 | −1.83632 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.89074 | −0.465633 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.19340 | −0.349346 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.36899 | 0.627394 | 0.313697 | − | 0.949523i | \(-0.398432\pi\) | ||||
0.313697 | + | 0.949523i | \(0.398432\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.492939 | −0.0328626 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.87731 | 0.390091 | 0.195045 | − | 0.980794i | \(-0.437515\pi\) | ||||
0.195045 | + | 0.980794i | \(0.437515\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.4528 | −0.822903 | −0.411452 | − | 0.911432i | \(-0.634978\pi\) | ||||
−0.411452 | + | 0.911432i | \(0.634978\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.5448 | −0.887350 | −0.443675 | − | 0.896188i | \(-0.646325\pi\) | ||||
−0.443675 | + | 0.896188i | \(0.646325\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.9493 | −0.844722 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.27290 | 0.0826838 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.28427 | 0.471180 | 0.235590 | − | 0.971853i | \(-0.424298\pi\) | ||||
0.235590 | + | 0.971853i | \(0.424298\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.31710 | 0.213673 | 0.106837 | − | 0.994277i | \(-0.465928\pi\) | ||||
0.106837 | + | 0.994277i | \(0.465928\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.2935 | −1.36598 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.44350 | 0.282733 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −16.6377 | −1.05437 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.3120 | −0.903367 | −0.451683 | − | 0.892178i | \(-0.649176\pi\) | ||||
−0.451683 | + | 0.892178i | \(0.649176\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.7191 | 0.673901 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 15.7599 | 0.986923 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −29.6916 | −1.85211 | −0.926056 | − | 0.377387i | \(-0.876823\pi\) | ||||
−0.926056 | + | 0.377387i | \(0.876823\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 31.6802 | 1.96095 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.9460 | 0.736624 | 0.368312 | − | 0.929702i | \(-0.379936\pi\) | ||||
0.368312 | + | 0.929702i | \(0.379936\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −17.7916 | −1.09293 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −41.9836 | −2.56936 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.76168 | 0.534209 | 0.267105 | − | 0.963668i | \(-0.413933\pi\) | ||||
0.267105 | + | 0.963668i | \(0.413933\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.34066 | 0.567405 | 0.283702 | − | 0.958912i | \(-0.408437\pi\) | ||||
0.283702 | + | 0.958912i | \(0.408437\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.291819 | 0.0175974 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 32.2328 | 1.93668 | 0.968340 | − | 0.249635i | \(-0.0803106\pi\) | ||||
0.968340 | + | 0.249635i | \(0.0803106\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.14524 | 0.367906 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.0271 | −0.657822 | −0.328911 | − | 0.944361i | \(-0.606682\pi\) | ||||
−0.328911 | + | 0.944361i | \(0.606682\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.96162 | −0.473269 | −0.236635 | − | 0.971599i | \(-0.576044\pi\) | ||||
−0.236635 | + | 0.971599i | \(0.576044\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −13.4842 | −0.798737 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.9450 | −0.702648 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.0360 | −0.646940 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.5374 | −1.02455 | −0.512273 | − | 0.858823i | \(-0.671196\pi\) | ||||
−0.512273 | + | 0.858823i | \(0.671196\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 26.0900 | 1.51902 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 51.6761 | 2.99855 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.00239 | −0.347127 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.15582 | 0.411091 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.5728 | 0.948958 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 28.8642 | 1.64737 | 0.823683 | − | 0.567051i | \(-0.191916\pi\) | ||||
0.823683 | + | 0.567051i | \(0.191916\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −32.4493 | −1.84598 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.3112 | −0.698106 | −0.349053 | − | 0.937103i | \(-0.613497\pi\) | ||||
−0.349053 | + | 0.937103i | \(0.613497\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.6368 | −0.714273 | −0.357136 | − | 0.934052i | \(-0.616247\pi\) | ||||
−0.357136 | + | 0.934052i | \(0.616247\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 29.6687 | 1.66636 | 0.833181 | − | 0.553000i | \(-0.186517\pi\) | ||||
0.833181 | + | 0.553000i | \(0.186517\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −18.7546 | −1.05006 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 36.8934 | 2.05919 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.32507 | −0.240654 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.163411 | −0.00906441 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 46.0292 | 2.54542 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.94401 | −0.161817 | −0.0809087 | − | 0.996722i | \(-0.525782\pi\) | ||||
−0.0809087 | + | 0.996722i | \(0.525782\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 49.3899 | 2.70655 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.52584 | 0.192637 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 21.3836 | 1.16484 | 0.582418 | − | 0.812889i | \(-0.302107\pi\) | ||||
0.582418 | + | 0.812889i | \(0.302107\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.5784 | −0.737476 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.63797 | −0.197007 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 18.2148 | 0.980654 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 25.3614 | 1.36147 | 0.680736 | − | 0.732529i | \(-0.261660\pi\) | ||||
0.680736 | + | 0.732529i | \(0.261660\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.63010 | 0.354901 | 0.177451 | − | 0.984130i | \(-0.443215\pi\) | ||||
0.177451 | + | 0.984130i | \(0.443215\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −28.9373 | −1.54456 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 27.0903 | 1.44187 | 0.720936 | − | 0.693001i | \(-0.243712\pi\) | ||||
0.720936 | + | 0.693001i | \(0.243712\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 19.4456 | 1.03207 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.6399 | 0.983774 | 0.491887 | − | 0.870659i | \(-0.336307\pi\) | ||||
0.491887 | + | 0.870659i | \(0.336307\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.2994 | −0.805234 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.9926 | −0.996853 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.84567 | 0.253634 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.23109 | −0.0642624 | −0.0321312 | − | 0.999484i | \(-0.510229\pi\) | ||||
−0.0321312 | + | 0.999484i | \(0.510229\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.96793 | −0.362736 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.7085 | 0.709798 | 0.354899 | − | 0.934905i | \(-0.384515\pi\) | ||||
0.354899 | + | 0.934905i | \(0.384515\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 35.5439 | 1.83548 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.5021 | 0.540885 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.85583 | −0.146694 | −0.0733471 | − | 0.997306i | \(-0.523368\pi\) | ||||
−0.0733471 | + | 0.997306i | \(0.523368\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −54.6997 | −2.80235 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.5276 | 0.537938 | 0.268969 | − | 0.963149i | \(-0.413317\pi\) | ||||
0.268969 | + | 0.963149i | \(0.413317\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −84.5045 | −4.29561 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.5333 | −0.534060 | −0.267030 | − | 0.963688i | \(-0.586042\pi\) | ||||
−0.267030 | + | 0.963688i | \(0.586042\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.84242 | 0.295464 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −26.8716 | −1.35549 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.895123 | −0.0450385 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.0280 | 0.704043 | 0.352022 | − | 0.935992i | \(-0.385494\pi\) | ||||
0.352022 | + | 0.935992i | \(0.385494\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.8036 | 1.28857 | 0.644286 | − | 0.764785i | \(-0.277155\pi\) | ||||
0.644286 | + | 0.764785i | \(0.277155\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.03717 | 0.101479 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 41.4026 | 2.05731 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −29.2387 | −1.44931 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.9885 | 1.73007 | 0.865036 | − | 0.501710i | \(-0.167296\pi\) | ||||
0.865036 | + | 0.501710i | \(0.167296\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 62.2660 | 3.07135 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.6999 | 0.574324 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.80600 | 0.431232 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −11.9556 | −0.584068 | −0.292034 | − | 0.956408i | \(-0.594332\pi\) | ||||
−0.292034 | + | 0.956408i | \(0.594332\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.73209 | 0.474313 | 0.237157 | − | 0.971471i | \(-0.423785\pi\) | ||||
0.237157 | + | 0.971471i | \(0.423785\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −40.6407 | −1.97602 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.159056 | 0.00771534 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 30.0828 | 1.45241 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.4751 | −0.504570 | −0.252285 | − | 0.967653i | \(-0.581182\pi\) | ||||
−0.252285 | + | 0.967653i | \(0.581182\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.7632 | 0.709476 | 0.354738 | − | 0.934966i | \(-0.384570\pi\) | ||||
0.354738 | + | 0.934966i | \(0.384570\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −31.8696 | −1.52803 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.99880 | −0.239125 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.1915 | −1.20232 | −0.601161 | − | 0.799128i | \(-0.705295\pi\) | ||||
−0.601161 | + | 0.799128i | \(0.705295\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.308041 | 0.0146355 | 0.00731774 | − | 0.999973i | \(-0.497671\pi\) | ||||
0.00731774 | + | 0.999973i | \(0.497671\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 29.5235 | 1.39955 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 61.6970 | 2.91817 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 36.1781 | 1.70735 | 0.853676 | − | 0.520804i | \(-0.174368\pi\) | ||||
0.853676 | + | 0.520804i | \(0.174368\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.12500 | 0.194239 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.2875 | −0.765252 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.1807 | −1.13113 | −0.565563 | − | 0.824705i | \(-0.691341\pi\) | ||||
−0.565563 | + | 0.824705i | \(0.691341\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 28.1661 | 1.31468 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.3173 | 0.713398 | 0.356699 | − | 0.934219i | \(-0.383902\pi\) | ||||
0.356699 | + | 0.934219i | \(0.383902\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.79929 | 0.223042 | 0.111521 | − | 0.993762i | \(-0.464428\pi\) | ||||
0.111521 | + | 0.993762i | \(0.464428\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.18199 | −0.286683 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.3349 | 1.03353 | 0.516767 | − | 0.856126i | \(-0.327135\pi\) | ||||
0.516767 | + | 0.856126i | \(0.327135\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −59.2342 | −2.72937 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 50.0266 | 2.30022 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.136089 | −0.00624419 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −55.8377 | −2.55663 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.1981 | 1.01426 | 0.507128 | − | 0.861871i | \(-0.330707\pi\) | ||||
0.507128 | + | 0.861871i | \(0.330707\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.3729 | 0.746540 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.76066 | 0.352393 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −33.4536 | −1.51593 | −0.757963 | − | 0.652297i | \(-0.773805\pi\) | ||||
−0.757963 | + | 0.652297i | \(0.773805\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 66.0609 | 2.98738 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.3600 | 1.64090 | 0.820451 | − | 0.571717i | \(-0.193722\pi\) | ||||
0.820451 | + | 0.571717i | \(0.193722\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10.2222 | −0.460384 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −63.8144 | −2.86824 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.134195 | 0.00600738 | 0.00300369 | − | 0.999995i | \(-0.499044\pi\) | ||||
0.00300369 | + | 0.999995i | \(0.499044\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 37.7383 | 1.68602 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.13202 | 0.184238 | 0.0921189 | − | 0.995748i | \(-0.470636\pi\) | ||||
0.0921189 | + | 0.995748i | \(0.470636\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.03208 | −0.223925 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 24.1981 | 1.07467 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 42.7673 | 1.89563 | 0.947815 | − | 0.318822i | \(-0.103287\pi\) | ||||
0.947815 | + | 0.318822i | \(0.103287\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −24.0990 | −1.06400 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 22.8189 | 1.00552 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.0592 | 1.05812 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.5906 | −0.816035 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.13363 | −0.0934762 | −0.0467381 | − | 0.998907i | \(-0.514883\pi\) | ||||
−0.0467381 | + | 0.998907i | \(0.514883\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 43.5611 | 1.90479 | 0.952396 | − | 0.304863i | \(-0.0986108\pi\) | ||||
0.952396 | + | 0.304863i | \(0.0986108\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.98287 | −0.0863754 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.2475 | −0.706413 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 81.8816 | 3.55336 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.30989 | −0.100053 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −25.9440 | −1.12166 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −35.3352 | −1.52483 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 40.0196 | 1.72058 | 0.860289 | − | 0.509806i | \(-0.170283\pi\) | ||||
0.860289 | + | 0.509806i | \(0.170283\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −46.3950 | −1.99100 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −32.3684 | −1.38651 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.5014 | 1.00485 | 0.502423 | − | 0.864622i | \(-0.332442\pi\) | ||||
0.502423 | + | 0.864622i | \(0.332442\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 52.0127 | 2.21985 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.74615 | 0.372599 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −49.6852 | −2.10902 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 33.9635 | 1.43908 | 0.719539 | − | 0.694452i | \(-0.244353\pi\) | ||||
0.719539 | + | 0.694452i | \(0.244353\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −28.0135 | −1.18485 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −29.2811 | −1.23625 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −45.3615 | −1.91176 | −0.955880 | − | 0.293757i | \(-0.905094\pi\) | ||||
−0.955880 | + | 0.293757i | \(0.905094\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.54852 | 0.401709 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.7354 | 0.827350 | 0.413675 | − | 0.910425i | \(-0.364245\pi\) | ||||
0.413675 | + | 0.910425i | \(0.364245\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.8619 | 0.873043 | 0.436522 | − | 0.899694i | \(-0.356210\pi\) | ||||
0.436522 | + | 0.899694i | \(0.356210\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.53749 | −0.231332 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.183832 | 0.00766634 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.1897 | −0.465832 | −0.232916 | − | 0.972497i | \(-0.574827\pi\) | ||||
−0.232916 | + | 0.972497i | \(0.574827\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −32.5625 | −1.35325 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 33.0559 | 1.36903 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 35.7343 | 1.47743 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.93067 | 0.120962 | 0.0604808 | − | 0.998169i | \(-0.480737\pi\) | ||||
0.0604808 | + | 0.998169i | \(0.480737\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.69656 | 0.0699054 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21.1258 | 0.869001 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −38.4675 | −1.57967 | −0.789835 | − | 0.613320i | \(-0.789834\pi\) | ||||
−0.789835 | + | 0.613320i | \(0.789834\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 38.4777 | 1.57479 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 34.8868 | 1.42544 | 0.712719 | − | 0.701450i | \(-0.247464\pi\) | ||||
0.712719 | + | 0.701450i | \(0.247464\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.5920 | 0.880757 | 0.440379 | − | 0.897812i | \(-0.354844\pi\) | ||||
0.440379 | + | 0.897812i | \(0.354844\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.0656 | 0.450626 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 13.3559 | 0.542994 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −31.5921 | −1.28228 | −0.641142 | − | 0.767422i | \(-0.721539\pi\) | ||||
−0.641142 | + | 0.767422i | \(0.721539\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.4725 | −0.545040 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −18.7893 | −0.758894 | −0.379447 | − | 0.925213i | \(-0.623886\pi\) | ||||
−0.379447 | + | 0.925213i | \(0.623886\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.00960 | 0.282654 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.4135 | 0.620526 | 0.310263 | − | 0.950651i | \(-0.399583\pi\) | ||||
0.310263 | + | 0.950651i | \(0.399583\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.61805 | 0.145422 | 0.0727108 | − | 0.997353i | \(-0.476835\pi\) | ||||
0.0727108 | + | 0.997353i | \(0.476835\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 32.5535 | 1.30633 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.6413 | −0.985651 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 25.0530 | 1.00052 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15.9366 | −0.635432 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.0390 | 1.39488 | 0.697441 | − | 0.716642i | \(-0.254322\pi\) | ||||
0.697441 | + | 0.716642i | \(0.254322\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −59.3467 | −2.35882 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 38.4656 | 1.52646 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 61.0288 | 2.41426 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.26732 | 0.0500562 | 0.0250281 | − | 0.999687i | \(-0.492032\pi\) | ||||
0.0250281 | + | 0.999687i | \(0.492032\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.98105 | −0.156997 | −0.0784986 | − | 0.996914i | \(-0.525013\pi\) | ||||
−0.0784986 | + | 0.996914i | \(0.525013\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 85.0099 | 3.34726 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.0142 | 0.944097 | 0.472049 | − | 0.881573i | \(-0.343515\pi\) | ||||
0.472049 | + | 0.881573i | \(0.343515\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −48.4738 | −1.90276 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25.6864 | 1.00518 | 0.502592 | − | 0.864523i | \(-0.332380\pi\) | ||||
0.502592 | + | 0.864523i | \(0.332380\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.8965 | 0.738348 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 15.2078 | 0.593313 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.4949 | 0.681505 | 0.340753 | − | 0.940153i | \(-0.389318\pi\) | ||||
0.340753 | + | 0.940153i | \(0.389318\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.6256 | 1.26899 | 0.634494 | − | 0.772928i | \(-0.281209\pi\) | ||||
0.634494 | + | 0.772928i | \(0.281209\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 16.3966 | 0.636792 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −11.8145 | −0.457460 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −29.5798 | −1.14362 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −30.7915 | −1.18869 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.92133 | −0.305345 | −0.152672 | − | 0.988277i | \(-0.548788\pi\) | ||||
−0.152672 | + | 0.988277i | \(0.548788\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.886248 | 0.0341117 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.1753 | 1.15973 | 0.579866 | − | 0.814712i | \(-0.303105\pi\) | ||||
0.579866 | + | 0.814712i | \(0.303105\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.5558 | −0.711062 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.4402 | −0.629066 | −0.314533 | − | 0.949247i | \(-0.601848\pi\) | ||||
−0.314533 | + | 0.949247i | \(0.601848\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −43.7864 | −1.67299 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 39.3160 | 1.50000 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −18.5104 | −0.705190 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 51.1349 | 1.94526 | 0.972631 | − | 0.232354i | \(-0.0746428\pi\) | ||||
0.972631 | + | 0.232354i | \(0.0746428\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.19252 | −0.234896 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.24833 | 0.0851616 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 42.7637 | 1.61747 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.11382 | 0.268685 | 0.134343 | − | 0.990935i | \(-0.457108\pi\) | ||||
0.134343 | + | 0.990935i | \(0.457108\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.6354 | 0.514268 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 40.8837 | 1.53977 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.9782 | 1.12585 | 0.562927 | − | 0.826507i | \(-0.309675\pi\) | ||||
0.562927 | + | 0.826507i | \(0.309675\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.80928 | −0.105356 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.29175 | −0.0858267 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −21.1547 | −0.791140 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −22.9979 | −0.858872 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.9726 | −0.782147 | −0.391074 | − | 0.920359i | \(-0.627896\pi\) | ||||
−0.391074 | + | 0.920359i | \(0.627896\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −10.4728 | −0.389486 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.321642 | −0.0119455 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.7303 | 0.991372 | 0.495686 | − | 0.868502i | \(-0.334917\pi\) | ||||
0.495686 | + | 0.868502i | \(0.334917\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 11.2834 | 0.417903 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 27.2670 | 1.00850 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.1849 | 0.745545 | 0.372772 | − | 0.927923i | \(-0.378407\pi\) | ||||
0.372772 | + | 0.927923i | \(0.378407\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.55082 | −0.241303 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −47.8248 | −1.75926 | −0.879632 | − | 0.475655i | \(-0.842211\pi\) | ||||
−0.879632 | + | 0.475655i | \(0.842211\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −14.0290 | −0.515369 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −42.2673 | −1.55064 | −0.775318 | − | 0.631571i | \(-0.782411\pi\) | ||||
−0.775318 | + | 0.631571i | \(0.782411\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −43.3863 | −1.58955 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 36.7192 | 1.34349 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.6944 | −1.08357 | −0.541783 | − | 0.840519i | \(-0.682250\pi\) | ||||
−0.541783 | + | 0.840519i | \(0.682250\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 45.1859 | 1.64667 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.4536 | 0.416839 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.17713 | 0.260857 | 0.130429 | − | 0.991458i | \(-0.458365\pi\) | ||||
0.130429 | + | 0.991458i | \(0.458365\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −33.8422 | −1.22840 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.3861 | −0.956496 | −0.478248 | − | 0.878225i | \(-0.658728\pi\) | ||||
−0.478248 | + | 0.878225i | \(0.658728\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −34.7820 | −1.25755 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 27.1440 | 0.980114 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −41.9486 | −1.51270 | −0.756352 | − | 0.654164i | \(-0.773020\pi\) | ||||
−0.756352 | + | 0.654164i | \(0.773020\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 93.7424 | 3.37605 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −22.6024 | −0.812951 | −0.406476 | − | 0.913662i | \(-0.633242\pi\) | ||||
−0.406476 | + | 0.913662i | \(0.633242\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.0623914 | −0.00224116 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.92368 | −0.0689231 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −36.1290 | −1.29280 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −56.9573 | −2.03549 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 41.6544 | 1.48671 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.45290 | 0.265667 | 0.132834 | − | 0.991138i | \(-0.457592\pi\) | ||||
0.132834 | + | 0.991138i | \(0.457592\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −37.7161 | −1.34273 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 17.2424 | 0.612296 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 56.1717 | 1.99220 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −38.3124 | −1.35710 | −0.678548 | − | 0.734556i | \(-0.737391\pi\) | ||||
−0.678548 | + | 0.734556i | \(0.737391\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.1135 | 0.463921 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 92.6576 | 3.27389 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.00300 | −0.317709 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −27.6624 | −0.973762 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.5594 | −0.476723 | −0.238362 | − | 0.971176i | \(-0.576610\pi\) | ||||
−0.238362 | + | 0.971176i | \(0.576610\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.3823 | 0.364572 | 0.182286 | − | 0.983246i | \(-0.441650\pi\) | ||||
0.182286 | + | 0.983246i | \(0.441650\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −29.4904 | −1.03427 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −46.4550 | −1.62725 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −23.3297 | −0.816204 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.4003 | −0.816675 | −0.408337 | − | 0.912831i | \(-0.633891\pi\) | ||||
−0.408337 | + | 0.912831i | \(0.633891\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.66810 | −0.0581465 | −0.0290732 | − | 0.999577i | \(-0.509256\pi\) | ||||
−0.0290732 | + | 0.999577i | \(0.509256\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.921332 | −0.0320767 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.7281 | −0.477373 | −0.238686 | − | 0.971097i | \(-0.576717\pi\) | ||||
−0.238686 | + | 0.971097i | \(0.576717\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.6716 | −0.613761 | −0.306880 | − | 0.951748i | \(-0.599285\pi\) | ||||
−0.306880 | + | 0.951748i | \(0.599285\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −101.765 | −3.53020 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −26.5381 | −0.918390 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −11.0484 | −0.381890 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.26376 | 0.250773 | 0.125386 | − | 0.992108i | \(-0.459983\pi\) | ||||
0.125386 | + | 0.992108i | \(0.459983\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.32871 | −0.287197 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 34.8148 | 1.19908 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −17.0164 | −0.585384 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 25.1365 | 0.862681 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.4190 | −0.631396 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 44.2376 | 1.51467 | 0.757333 | − | 0.653029i | \(-0.226502\pi\) | ||||
0.757333 | + | 0.653029i | \(0.226502\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 29.7596 | 1.01776 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −44.7732 | −1.52942 | −0.764711 | − | 0.644373i | \(-0.777119\pi\) | ||||
−0.764711 | + | 0.644373i | \(0.777119\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 32.7417 | 1.11713 | 0.558567 | − | 0.829460i | \(-0.311351\pi\) | ||||
0.558567 | + | 0.829460i | \(0.311351\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.500831 | 0.0170485 | 0.00852424 | − | 0.999964i | \(-0.497287\pi\) | ||||
0.00852424 | + | 0.999964i | \(0.497287\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.0732 | 0.444501 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 37.7128 | 1.28079 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.66309 | 0.0564165 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.66829 | 0.124295 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 24.3563 | 0.824336 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.6696 | 1.27201 | 0.636006 | − | 0.771684i | \(-0.280585\pi\) | ||||
0.636006 | + | 0.771684i | \(0.280585\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 55.3691 | 1.86755 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27.4049 | −0.923293 | −0.461647 | − | 0.887064i | \(-0.652741\pi\) | ||||
−0.461647 | + | 0.887064i | \(0.652741\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.0131 | −0.639842 | −0.319921 | − | 0.947444i | \(-0.603656\pi\) | ||||
−0.319921 | + | 0.947444i | \(0.603656\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −82.3713 | −2.76888 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.3297 | −0.917643 | −0.458821 | − | 0.888529i | \(-0.651728\pi\) | ||||
−0.458821 | + | 0.888529i | \(0.651728\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −76.9239 | −2.57705 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11.2199 | −0.375461 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.8482 | 0.830585 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 18.9507 | 0.632747 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.00976 | 0.133733 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.0171 | 0.600236 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 32.6257 | 1.08451 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 52.7038 | 1.75000 | 0.875001 | − | 0.484121i | \(-0.160860\pi\) | ||||
0.875001 | + | 0.484121i | \(0.160860\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15.7929 | −0.523816 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 55.8154 | 1.84925 | 0.924623 | − | 0.380883i | \(-0.124380\pi\) | ||||
0.924623 | + | 0.380883i | \(0.124380\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.7377 | −0.719414 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −52.3238 | −1.72977 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −56.6479 | −1.86864 | −0.934321 | − | 0.356434i | \(-0.883992\pi\) | ||||
−0.934321 | + | 0.356434i | \(0.883992\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −91.1300 | −3.00284 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 20.2313 | 0.665920 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.501445 | −0.0164874 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 71.6155 | 2.35216 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.9807 | −0.918016 | −0.459008 | − | 0.888432i | \(-0.651795\pi\) | ||||
−0.459008 | + | 0.888432i | \(0.651795\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 38.8691 | 1.27252 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 20.5909 | 0.673394 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17.6255 | −0.575799 | −0.287900 | − | 0.957661i | \(-0.592957\pi\) | ||||
−0.287900 | + | 0.957661i | \(0.592957\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 39.8969 | 1.30198 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.16930 | −0.168514 | −0.0842572 | − | 0.996444i | \(-0.526852\pi\) | ||||
−0.0842572 | + | 0.996444i | \(0.526852\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.59856 | 0.0846207 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.1393 | 0.654441 | 0.327220 | − | 0.944948i | \(-0.393888\pi\) | ||||
0.327220 | + | 0.944948i | \(0.393888\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.04144 | 0.163652 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −93.6702 | −3.03747 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −44.3472 | −1.43655 | −0.718273 | − | 0.695761i | \(-0.755067\pi\) | ||||
−0.718273 | + | 0.695761i | \(0.755067\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.89405 | 0.126008 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 59.2121 | 1.91406 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.2222 | −0.974910 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −81.4235 | −2.62384 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.8985 | 0.737128 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 60.6168 | 1.94931 | 0.974653 | − | 0.223722i | \(-0.0718208\pi\) | ||||
0.974653 | + | 0.223722i | \(0.0718208\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13.6551 | 0.438666 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.0331 | 0.707075 | 0.353538 | − | 0.935420i | \(-0.384979\pi\) | ||||
0.353538 | + | 0.935420i | \(0.384979\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.515921 | 0.0165227 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −33.2759 | −1.06459 | −0.532296 | − | 0.846558i | \(-0.678671\pi\) | ||||
−0.532296 | + | 0.846558i | \(0.678671\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −54.8532 | −1.75311 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −101.586 | −3.24339 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −61.0791 | −1.94812 | −0.974061 | − | 0.226285i | \(-0.927342\pi\) | ||||
−0.974061 | + | 0.226285i | \(0.927342\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.8560 | −0.473352 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 31.5144 | 1.00210 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.0442 | 0.986151 | 0.493075 | − | 0.869987i | \(-0.335873\pi\) | ||||
0.493075 | + | 0.869987i | \(0.335873\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.29483 | 0.294963 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −27.0581 | −0.857799 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.4932 | 0.839049 | 0.419525 | − | 0.907744i | \(-0.362197\pi\) | ||||
0.419525 | + | 0.907744i | \(0.362197\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −88.7974 | −2.80942 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8036.2.a.t.1.1 | yes | 20 | |
7.6 | odd | 2 | 8036.2.a.s.1.20 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8036.2.a.s.1.20 | ✓ | 20 | 7.6 | odd | 2 | ||
8036.2.a.t.1.1 | yes | 20 | 1.1 | even | 1 | trivial |